Equations of a plane

The three points A, B and C define a plane in space. The vectors AB and AC are two vectors that span the plane from the position vector of point A. The vector AD is the normal (perpendicular) to vectors AB and AC. Using the normal vector is another way to define a plane (see g). That is the Cartesian equation of a plane.
This page is a good starting point to investigate planes in 3D. You may start by adjusting the points to match any problem you are investigating.